Polymer optical fiber curvature measuring technique based on speckle pattern image processing

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UNIVERSIDADE FEDERAL DO ESP´IRITO SANTO CENTRO TECNOL ´OGICO

PROGRAMA DE P ÓS - GRADUA ¸C ÃO EM ENGENHARIA ELÉTRICA

CLEMENS H ¨AGELE

POLYMER OPTICAL FIBER CURVATURE

MEASURING TECHNIQUE BASED ON SPECKLE

PATTERN IMAGE PROCESSING

V´ITORIA 2015

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Dados Internacionais de Cataloga¸cão-na-publica¸cão (CIP) (Biblioteca Setorial Tecnológica,

Universidade Federal do Esp´ırito Santo, ES, Brasil)

H¨agele, Johann Clemens, 1984-H142p

Polymer optical fiber curvature measuring technique based on speckle pattern image processing / Johann Clemens H¨agele. – 2015.

156 f. : il.

Orientador: Anselmo Frizera Neto. Coorientador: Maria Jos´e Pontes.

Disserta¸cão (Mestrado em Engenharia Elétrica) – Universidade Federal do Esp´ırito Santo, Centro Tecnológico.

1. Speckle. 2. Processamento de imagens. 3. Fibras ópticas. 4. Pol´ımeros. 5. Reconhecimento de padrões. 6. Sensor de curvatura. I. Frizera Neto, Anselmo. II. Pontes, Maria José. III. Universidade Federal do Esp´ırito Santo. Centro Tecnológico. IV. T´ıtulo.

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CLEMENS H ¨AGELE

Disserta¸cão apresentada ao Programa de Pós -Gradua¸cão em Engenharia Elétrica – PPGEE, do Centro Tecnológico das Universidade Federal do Esp´ırito Santo – UFES, como requisito parcial para obten¸cão do Grau de Mestre em Engenharia Elétrica.

Orientador: Anselmo Frizera Neto Co - Orientadora: Maria Jos´e Pontes

V´ITORIA 2015

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CLEMENS H ¨AGELE

Disserta¸cão apresentada ao Programa de Pós-Gradua¸cão em Engenharia Elétrica – PPGEE, do Centro Tecnológico das Universidade Federal do Esp´ırito Santo – UFES, como requisito parcial para obten¸cão do Grau de Mestre em Engenharia Elétrica.

Aprovada em 15 de Outubro de 2015

BANCA EXAMINADORA

Prof. Dr. Anselmo Frizera Neto - Orientador Universidade Federal do Esp´ırito Santo – UFES

Profa. Dr. Maria Jos´e Pontes - Co - Orientadora Universidade Federal do Esp´ırito Santo – UFES

Prof. Dr. Alessandro Botti Benevides

Universidade Federal do Esp´ırito Santo – UFES

Prof. Dr. Paulo Fernando da Costa Antunes Universidade de Aveiro – UA

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Abstract

A self-developed light intensity-modulated curvature measuring principle for the measurement of bending angles within a range from −120◦ to +130◦ under appli-cation of a Polymer Optical Fiber is described in the present work. The determina-tion of the bending angle is based on the graphical analysis of the speckle-pattern that is affected by the curved fiber. The contours of speckles in a defined region of interest in the speckle-pattern are made visible by an edge-detection algorithm and their amount is set in relation to the bending angle. The digital image of a speckle-pattern represents a source of image information that facilitates the fur-ther analysis by a variety of image processing techniques. The purpose of this work is the evaluation of a graphical analysis of a speckle-pattern for the curva-ture measurement. The research incorporates the basic study of general effects on the fiber under curvature until the development of a final measurement setup that facilitates a reliable and precise measurement of the bending angle. Coherent light with a wavelength of 632.8 nm is propagated through a looped Polymer Optical Fiber and received by a 5-Megapixel Charge-Coupled-Device-camera, positioned on the fiber output face. An especially designed acrylic goniometer facilitates the defined bending of the fiber for different fiber loop configurations. Different fiber arrangements and spatial image filters are evaluated under consideration of preci-sion of bending angle gauging and computational efficiency. A developed digital signal processing routine performs a signal noise reduction and precision improve-ment for the bending angle measureimprove-ment. Practical results revealed the existence of a non-linear dependence in static and dynamic operation in the range from −120◦ _{to +130}◦ _{between the geometrical arrangements of the fiber, the average} pixel intensity, the amount of detected speckle contours and the bending angle. A potential application of the sensor for the measurement of human joint movement and posture in the medical field of rehabilitation is possible. The curvature mea-surement for an application in the robotic field or industrial application is also convenient.

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Acknowledgments

Firstly, I would like to thank my girlfriend Katia for the her patience, comprehen-sion, motivation and constant assistance during the work on the master thesis. I would like to thank my mother, my sister, my brother and my friends for their assistance and steady motivation meanwhile writing on the master thesis.

Gratitude is dedicated to the coordinator of the Postgraduate Program in Electri-cal Engineering, Mois´es Renato Nunes Ribeiro, for making the Post-Graduation at Universidade Federal do Esp´ırito Santo possible. I want to thank my supervisor Anselmo Frizera Neto and Co-Supervisor Maria Jos´e Pontes for their technical orientation and support during the work on the master thesis.

In thanks to Laboratório de Telecomunica¸cões (LABTEL) from Universidade Fed-eral do Esp´ırito Santo (UFES) for the opportunity to study in Brazil. Gratitude to Funda¸cão de Amparo à Pesquisa do Esp´ırito Santo (FAPES) for the scholar-ship. Thanks to Petrobras, Coordena¸cão de Aperfei¸coamento de Pessoal de N´ıvel Superior (CAPES) for the financial support of the project.

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1. Introduction

1.1. Motivation

The application of Polymer Optical Fiber-based sensors became more attractive in the last few years according to the improvement of the highly complex manu-facturing process and material compositions of the Polymer Optical Fiber (POF). POF-based sensor applications can be found in the industry, the domestic, medi-cal, aerospace, automobile field. POF-curvature sensors based on light intensity-modulation are increasingly utilized in the field of human joint movement analysis by the advantageously characteristics such as lightweight, cost efficiency, mechani-cal robustness, electromagnetic interference immunity and simplicity in application [1], [2].

Angular joint movement in static operation is analyzable by radiographic and stereo radiographic imaging technology, characterized by highly time consum-ing, technically complex and harmful by the fact of the patients repeated X-ray-exposure. Non-invasive skin-mounted sensor concepts that are utilized to exami-nation of limb curvature in static operation are the spinal mouse, flexible curves, electromagnetic and and gyroscope sensors [3], [4].

The well-established measuring technique for angular joint movement in dynamic operation, composed of CCD-cameras and reflecting markers is characterized by high installation effort and complexity [4].

A reliable high precision curvature sensor based on light intensity-modulation to gauge the dynamic angles of a human knee joint is presented in [5]. The char-acteristic curve possess an exponential dependence in the range from −125◦ to +125◦ and a linear range between −45◦ and +25◦, as depicted on figure 1.1. The fiber core is provided with a Sensitive Zone consisting of grinded fine cavities in a defined pattern. The manufacturing process is highly precise and needs special tools and equipment. A stronger signal attenuation is induced by the removal of

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the cladding and the bending direction of the fiber is detectable while the me-chanical flexibility and robustness is limited. A cracking at a bending angle of 140◦ is reported in [5]. The generated curvature data is transmitted via ZigBee to a personal computer for its analysis and documentation. The signal response as a function of the bending angle represents high precision and stability. The perturbation by loose parts of the fiber between the knee joint and the control device weared on the persons waist were noticed.

Figure 1.1: Knee curvature sensor: a) Measurement setup b) Attachment of curvature sensor on human body c) Signal output as a function of the bending angle, adapted from [5].

The constant movement of the limb and the body makes the attachment of the curvature sensor on the human body challenging. The curvature sensor has to resist the movement of the leg in the three dimensions and the body movement in the sagittal and frontal plane, in case of a knee curvature sensor.

Several researches proved that the signal attenuation of a curved fiber in rela-tion to the bending angle is non-linear [2], [6], [5], [7], [8], [9], [10], [11]. The mechanical manipulation of the fiber has no influence on shape of the non-linear characteristic curve. The mechanical robustness and flexibility is preserved for a non-manipulated fiber while the sensor sensitivity is comparatively low.

Speckles are defined as Modal Noise in literature and the time-varying intensi-ties of the speckles inside the speckle-pattern represent a challenging task for the image information extraction [6]. The bending shape of the fiber is indicated as non-linear and depends mainly on the stiffness of the fiber as described in [10] and [7]. Measurement setups that intend to generate a defined bending at a constant bending radius and changing bending angle is presented in [11] and [12]. The extensive measurement setups are characterized by highly precise results. The

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bending characteristic depends on the bending radius, bending angle, tempera-ture, material properties of fiber. The signal attenuation as a function of the bending angle is influenced for an alteration of one of these parameters [6], [2].

In the present work, coherent light with a wavelength of 632.8 nm is propagated through a looped Polymeric Optical Fiber and received by a Charge-Coupled-Device camera positioned on the fiber back-end. An embedded system provided with a 5-Megapixel CCD-Camera controls acquisition parameters and transmits the image data via TCP/IP to a desktop computer for subsequent image process-ing tasks. The contours of speckles in a defined region of interest in the speckle-pattern are made visible by an edge-detection algorithm and their amount is set in relation to the bending angle. The signal response is compared to the commonly known speckle image processing technique Speckle Mean Intensity Variation as presented in [13].

All components are mounted on a self-developed acrylic goniometer that facilitates the defined bending of the fiber. Different fiber loop arrangements, spatial image filters and speckle image processing techniques are examined under consideration of precision for the bending angle gauging and computing efficiency. Digital Sig-nal Processing (DSP) routines were developed for noise suppression and precision improvement for the bending angle measurement. The wireless sensor concept as presented in [5] represents a possible application example for the present measure-ment method.

A potential application for the measurement of human joint movement and pos-ture in the medical field of rehabilitation is possible. Industrial tasks in the robotic field application would be convenient.

1.2. Scope of The Work

The present research investigates the influence of a curved polymer optical fiber on a speckle-pattern for the measurement of the bending angle in the range from −120◦ _{to 130}◦_{. The speckle-pattern is analyzed graphically with a self-developed}

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arrangement of image processing techniques and digital signal processing routines. An elementary measurement setup consisting of an acrylic goniometer, a He-Ne-Laser to provide light with a wavelength of 632.8 nm, a 5-Megapixel CCD-camera and a polymer optical fiber produces reliable and stable measurement results of the bending angle . Several parameters in the experimental setup such as spatial image filters, addition of a polarizer, amount of fiber loops and image parameters are varied for a detailed system identification. The general influences of temperature and mechanical perturbations on the measurement setup will be investigated.

1.3. Objectives

A new method for the curvature analysis based on the graphical analysis of speckle-pattern variation is evaluated and described in the present work. The application of image processing stages facilitates the detection and counting of speckle con-tours in a defined region of interest of the speckle-pattern.

An experimental setup that enables the examination of the sensor principle for future application in the analysis of human joint movement analysis has to be cre-ated. The setup has to include the attachment of different fiber arrangements, an embedded system and, a CCD-camera and their power supply. The experimental setup should produce a uniform shape of the bent fiber to ensure a precise bending angle measurement.

A system description of the experimental setup that facilitates the determina-tion of disturbances on the speckle-pattern during fiber bending has to be de-veloped and therefore new types or similar experimental setups characterized by high precision can be developed. The optimum fiber arrangement that facilitates a compromise between adequate signal variation and feasibility in implementation for the measurement of bending angle has to be determined.

Influences of image processing stages such as spatial filtering methods and edge-detection parameters has to be determined thus a defined configuration for the image processing steps can be developed. The variation in amount of detected

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contours induced by a curved fiber must be studied for different external influences such as temperature and mechanical waves. A detailed analysis of the output sig-nal has to be performed for the subsequent filtering process that incorporates noise reduction and precise determination of bending angle.

A final comparison to the commonly known speckle image processing technique Mean Speckle Intensity Variation has to be made for an qualitative evaluation of the proposed speckle measuring technique.

1.4. Document Structure

The light propagation in the POF is a physical process which knowledge is essential for the present work, as presented in section 2.2. Speckle-patterns are graphically analyzed by image processing techniques. The origin of speckles and their main properties are reported in section 2.5. Further explanations of the curvature effects on the light propagation in chapter 2.6 are based on the physical theories of light propagation. Different physical mechanisms of signal attenuation and signal losses of the Polymer Optical Fiber are explained in section 2.3. An overview of the POF-based sensors demonstrates the variety of their application and working principles that are relevant for the present project. The sensor overview includes: POF-based sensors based on the graphical speckle-pattern analysis, curvature sensors based on light intensity modulation in general and for the analysis of joint movements, common techniques for the analysis of human joint movements, POF-based sensor for the analysis of human knee joint movement. The entire experimental design, including the images processing routine, for the curvature analysis is presented in chapter 3. An improved measurement setup based on the system identification analysis performed in section 4.2.3 is presented in subsection 3.3.1. The measure-ment results and the detailed interpretation are listed in section 4.1. The final measurement curves, processed by a self-developed digital signal processing pro-cedures are illustrated in chapter 5. The final chapter 6 summarizes the projects success and gives some proposals for further research directions and possibilities.

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2. Properties of Polymer Optical Fiber

2.1. The Multimode Polymer Optical Fiber

The ray path inside the fiber core is defined by the characteristic of the fiber such as Singlemode or Multimode fiber. The Singlemode fiber consists of a relatively thin core, even ten times thinner than the Multimode core, where the wave model of light is applied for the calculation of modes. The core diameter of the Multi-mode fiber type is sufficient for the analysis of the ray paths under assumption of the geometric ray-tracing model [2]. The Normalized Frequency determines the separation between both fiber groups.

The designation of the fiber type belongs firstly to the type of mode propaga-tion inside the core such as Singlemode or Multimode and secondly on the type of refraction of modes, affected by the structure of the refractive index profile. The main refractive profiles of Polymethyl Metacrylate (PMMA)-POF Multimode fibers are: Step-Index (SI), Multi-Step-Index (MSI) and Graded-Index (GI). The Multimode PMMA-POF that is utilized in the current work is characterized by a Step-Index Refractive Index Profile [6], [2], [14], [15].

The refractive index profile of the Multimode Step-Index Fiber is uniform over the whole fibers length. The light ray enters the Multimode Step-Index Fiber in-put face at an incident angle within the range of the acceptance angle and reflects totally at the core-cladding interface [6], [2], [14], [15].

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2.2. Light Propagation in POF

2.2.1. Total Reflection

The refractive index of the Core nco must be higher than the refractive index of the Cladding ncl, or nco> nclthus the conditions for a total reflection are given. In the contrary case of nco< ncl, interference is caused by induced Cladding Modes. The POF utilized in the current work owns a core refractive index of 1.49 and a cladding refractive index of 1.417. The refractive indexes of the core and the cladding depends on the material compositions and ambient influences such as temperature and humidity. The conditions of light propagation are determined by the ratio between core and cladding refractive indexes.

The light waves incident angle determines whether the light wave reflects totally or reflects partially on the core-cladding interface, as depicted on the following figure 2.2. For an ideal total reflection the incident angle β is the same as the angle of the refracted wave α. The angle of reflection depends on the order of the mode. Higher modes propagate under a large angle and lower modes under a lower angle of reflection. A total reflection is given when β > αmin where αmin is the incident angle for α0 = 90◦.

In the condition of an ideal total reflection, the incident angle is the same as the angle of reflection therefore the direction of propagation of the modes is towards the fibers end face.

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2.2.2. Numerical Aperture

The Numerical Aperture (NA) is considered as a main characteristic of the fiber and describes the capacity of light coupling on the input and the loss characteris-tics under curvature. A high value of the NA facilitates light coupling in a wide acceptance range.

Assuming the Snell’s law, when light enters with an incident angle of βmax and a refraction angle of αmax then:

n0· sin(βmax) = nco· sin(αmax) = nco· sin(90◦− γmax) (2.1)

n0· sin(βmax) = q (n2 co− n2cl) in Air n0 = 1 (2.2) sin(βmax) = q (n2 co− n2cl) (2.3)

βmax is defined as the Acceptance Angle or Aperture Angle and sets the maximum incident angle for a light wave in which the conditions for a total reflection is still given without loss by waves refraction. The range of acceptance is the Numerical Aperture and is defined as:

N A = sin(βmax) = q

n2

co− n2cl (2.4)

Figure 2.3: Illustration of numerical aperture, adapted from [6].

The fiber utilized in the current work is a Multimode Step-Index Polymer Optical Fiber, Model Eska Premier, fabricated by Mitsubishi Rayon Co. LTD and is char-acterized by a numerical aperture of 0.5 that corresponds to an acceptance angle of βmax = 30◦ [17]. The acceptance angle is comparatively high and facilitates the coupling of light into the fiber without any precise aligning with a light source or a

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receiver. Light enters the fiber in a defined angle range and exits the fibers output in a determined angle range as shown on figure 2.4.

Figure 2.4: Numerical aperture characteristic of fiber input and output, adapted from [16].

The POF owns the largest numerical aperture and diameter in comparison to other fiber types, such as glass or silica fibers, as depicted on the following figure 2.5 [16], [2], [6].

Figure 2.5: Numerical aperture of different fiber types [6].

2.2.3. The Mode Concept

Light waves are generally described as Mode Propagation in literature to discuss effects observed in the fiber optic propagation, which equations are derived by the Eigenvalue calculation of Maxwell’s equations. Wave paths are traceable and effects of attenuation within a relaxed and bend fiber are describable by the mode theories and physical approaches. The current section describes the modes and their main properties.

In order to propagate a light wave from the fiber input to the output, it must constructively overlap itself with the own reflection wave. Therefore, the phase position repeats after a double reflection [6]. The thick lines perpendicular to the direction of light propagation on figure 2.6 identify the planes of the same phase angle. The spacing between the lines is defined as _nλ

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Figure 2.6: Formation of mode structure within the fiber core [6].

2.2.4. Types of Modes

Radiation Modes are generated when the range of the acceptance angle for a total reflection is exceeded. Radiation modes cross the core-cladding interface and are absorbed by the cladding, as depicted on the following figure 2.7.

Cladding Modes are formed when the cladding refractive index is higher than the core refractive index. A minor part of the radiated modes continue travel-ing inside the claddtravel-ing. That specific type of light waves is designated as Skew Rays, Leaky Waves or Tunneling Rays and they are detectable even at more than twenty meters after the local of occurrence. This physical effect is considered as a disturbance and has significant influence on the signal quality in transmission and measurement. Radiation modes are not countable in contrary to guided modes [2], [6].

Figure 2.7: Types of modes, adapted from [6].

2.2.5. Number of Modes

As aforementioned, the type of light propagation inside the fibers core is grouped into the Singlemode- and Multimode-fibers. The Normalized Frequency determines the separation between both fiber groups and is defined as [6], [2]:

V = 2πρ λ ·

q (n2

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or by substituting the term (2.4) for the Numerical Aperture in (2.5) results in (2.6).

V = 2πρ

λ · N A (2.6)

where ρ is the fiber core radius and λ the wavelength. If the value of the Normal-ized Frequency V is lower than 2.405, only one mode is propagated, as in case of the Singlemode-fiber, otherwise more modes are propagated, as in case of a Mul-timode-fiber. A value of 2432.65 for the normalized frequency under assumption of the parameters from the currently utilized fiber was derived in chapter 2.6 in equation (2.20).

The number of modes N for a Multimode-Step-Index fiber is derived by (2.7) [2], [6]:

N = V 2

2 (2.7)

The number of modes N of a Multimode-Graded-Index fiber is defined as (2.8) [2], [6]:

N = V 2

4 (2.8)

The number of modes depends mainly on the refractive indexes that are included in the equation of the NA, as can be observed from the equations (2.7) and (2.8) [2], [6], [16]. The number of modes with the parameters of the utilized fiber in the project is calculated as 2.96 · 106 as described in chapter 2.6 from equation (2.23).

2.2.6. Mode Coupling

The core-cladding interface surface is provided with discontinuities that originate from the manufacturing process and the polymer characteristics. The disconti-nuities provoke minimal deviations of the refractive index in the core-cladding interface and produce scattering centers, as illustrated on figure 2.8 and figure 2.9. Signal losses are generated by scattered light waves. Mode Coupling depends on the angle of light propagation and coupling length of the fiber. This physical effect generates a considerable part of light attenuation in the fiber and causes Mode Dispersion which reduces the bandwidth [16], [2], [6].

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Figure 2.8: Mode coupling occurrence on scattering center, adapted from [6].

Figure 2.9: Mode coupling occurrence on core-cladding interface, adapted from [6].

2.2.7. Mode Conversion

Mode conversion arises in a curved fiber as in case of a microbend or macrobend and by fluctuations in the refractive index and is considered as a special condition of Mode Coupling.

Variations in the fiber position result in an altered reflection path of the light rays and generate losses by the presence of mode conversion. Mode calculation on a bent fiber is performed by the consideration of the cross-sections at the moments before and after bending. The fiber axis rotates by the amount of the bending angle as depicted on figure 2.10. An alteration of the light propagation direction leads to a rise in signal attenuation Lossintensity that amplifies for a higher bending angle αbent or diminished bending radius rbent, as described in the relations (2.9) [16], [2], [6].

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Figure 2.10: Mode propagation in the core of a curved fiber [6].

2.2.8. Mode-Dependent Attenuation

The material composition of the cladding is mainly responsible for Mode- Depen-dent Attenuation. A part of the electrical field escapes into the thinner cladding material by a distance in the order of the wavelength even in the conditions of a total reflection. That effect is also known as the Goos-H¨ahnchen-Shift.

A shift from the reflection plane into the optical thinner medium is the origin of this effect, as depicted on figure 2.11. The reflected light ray is slightly displaced on the core-cladding interface surface in the range of µm. The Goos-H¨ahnchen Shift is detectable in case of a reduced core diameter [16], [2], [6].

Figure 2.11: Mode dependent attenuation, Goos-H¨ahnchen Shift, adapted from [6].

2.3. Attenuation processes of the POF

The fibers physical characteristics include signal attenuation that is generated by the fiber characteristics such as length, core diameter, numerical aperture and wavelength.

Signal losses are induced by structural composition, external influences, internal material compositions fluctuations and impurities of the fiber.

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Signal losses are not influenced by the operator, where the signal attenuation can be partly influenced by the choice of the fiber main characteristics.

2.3.1. Signal Attenuation Induced by Fiber Length

The signal attenuation of the fiber rises with the length l of transmission, arising from Mode-Dependent Attenuation. The transmission loss P (l) in dependence with the fiber length l is defined as:

P (l) = P (0) · e−a0·l (2.10)

P (l) is the signal power at the fibers output at a fiber length of l in km and P (0) is the signal power on the fibers input at position 0. a0is the value of the Attenuation Coefficient in km−1 and commonly expressed logarithmic in dB/km [6], [2], [15].

Figure 2.12: Signal attenuation in relation to fiber length [6].

α = 10 l · log P (0) P (l) = 4, 343 · a0 (2.11)

The signal attenuation of the fiber utilized in the current work is 170 _kmdB at a wavelength of λ = 650 nm [17].

2.3.2. Signal Attenuation Induced by Numerical Aperture

The numerical aperture describes the Acceptance Angle in degree for that coupled light is still reflected totally inside the core. A high NA ensures a higher amount of light coupled into the fiber. A higher attenuation due to higher amount of refracting and radiating modes is provoked by this fact [6], [2], [15].

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2.3.3. Signal Attenuation Spectrum

The signal attenuation characteristics of a fiber as a function of the wavelength, determines the choice of light source for the transmitted signal. Material char-acteristics and compositions fluctuations are the origins of signal attenuation, as explained detailed in the following subsection 2.3.6. Impurities in the PMMA-material induce signal attenuation in the visible- and infrared- range of the light spectrum. Vibration Modes provoke attenuation in the red- and infrared-region of the light spectrum. Organic pollutants generate attenuation in the infrared range and electronic transitions of polymers in the region of ultraviolet light spectrum [6], [2], [15].

Figure 2.13: Attenuation spectrum of a PMMA-POF [6].

Figure 2.14: Attenuation spectrum of different standard-NA SI-POF (Measurement by POF-AC N¨urnberg) [6].

2.3.4. Overview of Loss Mechanisms

The fiber experiences different kinds of signal losses, originated by the material composition and imprecision in the manufacturing process. The type of signal losses is separated into two main categories:

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The Intrinsic losses and the Extrinsic losses. Each category is divided into sev-eral subdivisions, representing the origin of signal loss. Absorption, dispersion or radiation of the light rays are the physical mechanisms of signal loss, as depicted on the following figure 2.15.

Figure 2.15: Overview of losses and their attenuation mechanisms in the POF [2].

2.3.5. Intrinsic Losses

Intrinsic losses originate from the organic polymer composition and they are re-ducible by improvement of the manufacturing process. Intrinsic losses alter the refractive index of the fiber over the distances in the order of the wavelength. The Intrinsic losses summed up, compose the Ultimate Transmission Loss Limit [6], [2], [15]. The composition of the intrinsic losses is illustrated on the following figure 2.16.

Figure 2.16: Overview of intrinsic losses and their attenuation mechanisms in the POF [2].

2.3.6. Extrinsic Losses

The manufacturing process generates impurities and imperfections representing the extrinsic losses. The composition of the extrinsic losses is illustrated on the following figure 2.17.

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Figure 2.17: Overview of extrinsic losses and their attenuation mechanisms in the POF [2].

Absorption of light rays is induced by Transition Metals and Organic Pollutants. The transparency of the fibers core is reduced and the signal attenuation amplified by these impurities.

Dispersion of light rays according to Dust, Microfractures, Bubbles and Struc-tural Imperfections generates inhomogenities of the core transparency and signal attenuation.

Radiation of light rays is produced by Microbends and Macrobends [6], [2], [15]. By the fact of relevance of microbends on the present work it is described in the following section.

2.3.6.1. Microbends

Radiation of light waves are induced by microbends. They represent slight scale-fluctuations of the fiber axis in the order of the fiber diameter. Microbends are produced by defects in the manufacturing process and by non-uniform lateral pressure during the cabling process [6], [2], [15].

Figure 2.18: Microbends: a) Power loss from higher order modes b) Coupling to higher order modes, adapted from [2].

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2.4. Signal Attenuation Induced by Ambient

2.4.1. Temperature

The fiber expands in size and shape under increasing temperature conditions and affects the refractive index of the fiber. The fiber tension is reduced under higher temperatures and yields to a reduced signal attenuation under curvature. The transparency of the core material declines with an rising temperature. A POF-based temperature sensor takes advantage of this physical condition, as described in [2], [14]. Temperature and relative humidity are significantly responsible for the aging progress of the fiber [6], [2].

The physical definition of the temperature effect on the local numerical aperture for a straight and a bent fiber is described in [18] and [19]. The core refractive in-dex grows for higher temperatures and results in a higher numerical aperture and signal attenuation as described in [18]. The storage of the fiber in high temper-ature and constant high relative humidity causes constant aging of the fiber and destroys the internal structure of the POF. The signal attenuation lies in the range of 60 _kmdB for 1.000 h of storage at a temperature of +85◦ in a relative humidity of 95 %. The storage of the POF over a time range of 1000 h, a temperature rise from +80◦ to +85◦ causes an attenuation of 30 dB_km as illustrated on figure 2.19. The temperature is the major factor for the aging of the fiber as can be seen from the graph 2.19.

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2.4.2. Humidity

The absorption of water and humidity of the fiber leads to a reduced transparency of the core, causing higher signal attenuation, typically in the range of 10 _kmdB. The absorption process is reversible, hence the humidity is released in dry environment. The capacity of absorbing water rises for an increasing storing time in a dry environment of higher temperature in the range of 70◦. The attenuation of the currently utilized POF at 25◦ C is 170 _kmdB at a wavelength of 650 nm in a dry environment. The attenuation for the same temperature and wavelength in a relative humidity of 90 % rises to 190 _kmdB [6], [2].

2.5. Speckles

2.5.1. Formation of Speckles

A spatially coherent light source emits light waves with different but constant phases of the same frequency and amplitude through a Multicore POF. Micro-scopic scattering waves are generated when light waves travel against the optically rough surface of the fibers end face. The microscopic scattered light waves obtain a different phase in relation to the phase of the incident light wave. The dephased individual coherent wavelets interfere constructively in space, in equiphase, or destructively, in antiphase. A statistically intensity distributed granular spatial speckle-pattern is generated.

The speckle-pattern projected on the fiber end face, is temporally constant and spatially determined by the scattered surface structure, it is considered as a fin-gerprint of the micro structure. The reflection of a light ray on an optical rough surface erases the direction of preference. The surface roughness Rz is assumed as major than the wavelength λ of the light source. Rz > λ.

The surface roughness determines the structure of the speckle-pattern, in our case the fiber end face roughness.

Additional noise at the fiber end is caused when light is not transmitted at cou-pling points as depicted on the following figure 2.20. The phenomena of speckles in the specific case of Multimode fibers is described in this section [16], [2], [6].

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Figure 2.20: Modal noise at optical coupling point: a) Cross sections of two fibers b) Power loss diagram of optical coupling point, adapted from [6].

Speckle-patterns are producible by the illumination of optically rough surfaces by less coherent light sources like mercury lamps and laser diodes [20], [21].

Mechanical or temperature perturbations applied on the fiber sensing element induce a variation of the speckles in intensity, where the allover intensity of the speckle-pattern remains unchanged. The coherence of light and spectral width are the main influences on the speckle-patterns characteristics, besides the phase cor-relation between the modes. The structural distribution along the fiber provokes differential mode delay and spatial filtering [13]. Changes in speckle-patterns are analyzable by image processing techniques as described in section 3.5.

2.5.2. Statistical Intensity Distribution of a Speckle-Pattern

Speckles inside the speckle-pattern are stochastic spatially distributed and de-scribed quantitatively by probability and statistics. The emitted coherent laser light is linearly polarized. The speckle-patterns complex amplitude describes a circular Gaussian-statistic form in the complex plane. The intensity distribution of a speckle-pattern consists of a negative exponential probability, as illustrated on figure 2.22.

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Figure 2.21: Probability density function based on numerous measurements taken from a speckle-pattern [21].

The probability density function is given by:

p(I) = 1 hIi · exp −I hIi I ≥ 0 (2.13)

where hIi is the mean value of the speckle-pattern intensity. The most probable intensity of the speckle distribution on the image plane is zero.

2.5.3. Speckle Size

The number of modes in a Multimode-Step-Index Fiber is defined as:

N = V 2 2

The modes travel through the fibers core on different optical paths and interfere on the fibers end face constructively, or destructively, producing the characteristic granular speckle-pattern. The statistical average speckle size, received in a defined distance to the scattered field, in our case the fiber end face, is defined as:

ds ≈ 2.44 · λ · f

dco

(2.14)

where λ is the wavelength of propagated light, f the distance between the scattered field and the receiving image plane. dcois the fibers core diameter. The F-Number is a commonly applied quantity in literature and is defined as:

F = f dco

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The insertion of (2.15) in (2.14) results in (2.16).

ds ≈ 2.44 · λ · F (2.16)

The speckle size grows at an increasing wavelength λ and F-Number. The speckle size is an important parameter for image acquisitions and is adjustable by the aperture of the receiving lens.

Amount of Speckle in Speckle-Pattern

The total amount of bright and dark speckles in a defined speckle-pattern array is defined as:

Npattern =

N A2 · d2 co

λ (2.17)

where N A is the Numerical Aperture, dco the fiber core diameter and λ the wave-length of propagated light [13], [21].

Each image point of a speckle in an image plane results in an intensity distri-bution as illustrated on figure 2.22 for a diffraction. J1 is the Bessel-function of the first-order. α is the angle of diffracted light that deviates from the normal direction and is defined as α = dco

2 The Fraunhofer-diffraction function I yields the intensity distribution of the airy disk for perpendicular incidence [21], [22].

Figure 2.22: Speckle intensity distribution changing with the diffraction of a plane wave through a circular aperture [21].

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2.5.4. Speckle Measurement Methods

The measurement setup determines whether Subjective- Speckles or Objective-Speckles are produced. Objective-Speckles as depicted on figure 2.23 are induced in free space and defined as the Objective-Speckles or Far-Field-Speckles.

Figure 2.23: Formation of objective-speckles in free space [21].

A subjective-speckle-pattern as depicted on figure 2.24 is the recorded information of an imaging system that represents the major part of speckle occurrence by the fact of the commonly utilized CCD-cameras and digitalization of images.

Figure 2.24: Formation of subjective-speckles by imaging system [21].

Subjective-speckles are formed by the superposition of complex amplitudes that originate from the scattered wavelets in the image plane. Light beams reflected by the illuminated part of the object surface are captured as points on the image, arising from the pixel structure of the CCD-array. Therefore, the properties of the speckles depend on the scattered light collected by the image aperture and the properties of the image recording device. The speckle size is set by the spatial frequencies passing through the lens system [21]. The amount of deformation is deducible by the information of the change in speckle surface geometry and speckle surface intensity distribution, by comparison of speckle-patterns before and after a deformation. The research field Speckle Metrology incorporates the analysis of

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speckle-pattern properties by image processing methods and special measurement setups. 3D - deformation of objects under strain, pressure, temperature, vibration, static or dynamic loading is precisely measurable by observation and is known as Nondestructive Testing (NDT) or Nondestructive Evaluation (NDE)

Speckle Metrology is divided into two subdivisions:

The Speckle Interferometry (SI) describes the evaluation of changes in object sur-face intensity by the evaluation of the speckle intensity distribution and speckle phase inside a speckle-pattern, designated as means of first-order statistics.

Geometric changes of an object are grouped under Speckle Correlation and base upon the evaluation of the spatial structure of a speckle-pattern, the second-order statistics [21].

The previously described properties of speckles prove that the analysis of the speckle-pattern has to be realized by statistical methods and an appropriate imag-ing system for the exact speckle detection. The changes in the speckle-pattern by external influences are analyzed by graphical methods, based on statistical meth-ods and correlation algorithms. The present project demonstrates a measurement method that is based on the detection of the amount of speckle contours in a defined region of interest in the speckle-pattern to measure the bending angle of a curved POF.

2.6. Analysis of Fiber under Curvature

2.6.1. General Considerations of Fiber Curvature

The following explanation of the fiber bending process is applied to a Multimode Step-Index Polymer Optical Fiber (MSI-POF). Several researches that describe the effects on modes and signal attenuation of a curved fiber were realized, as for example in [23] where a three-dimensional analysis of a bent fiber is described and the redistribution of light power and radiated power are illustrated. The effect of the bending radius and the number of turns on the signal attenuation are investi-gated in [23].

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The influences of the bending radius on the power loss for different fiber core diameters is presented in [11]. The influence of number of turns, the bending ra-dius, the core diameter and the cladding thickness is presented in [9]. The results of the previously mentioned researches demonstrate the knowledge base for the present research.

At the beginning, the process of bending or curvature of the fiber is distinguished in different kinds of bending.

Static Bending is existent when the fiber is installed in locations like buildings or industrial production lines. An almost constant loss of light intensity is in-duced in that condition. The knowledge about the amount of signal attenuation is important for the planning of the power budget to ensure a sufficient energy transport over a defined fiber length [6].

The Minimum Bending Radius defines the radius for that the fiber is bendable over a short-time range without mechanical destruction or partially damage [6].

Repeated Bending is the case of the fiber bending for several times over a de-fined time without being mechanically destroyed or damaged. Some fibers has the requirement to tolerate bends in numbers of 105_{to 10}6_{[6]. The fiber utilized in this} present project posses a loss increment of less than 1 dB after 10.000 bendings [17].

Reel Change Bending arises particularly in drag chains in industrial installations [6].

Macrobends

Macrobends are assumed as bending radii that are significantly higher than the fibers core diameter. A decreasing bending radius generates an exponentially in-creasing radiation loss as depicted on the following figure 2.25. The signal loss of a bent Multimode-GI-POF is significantly higher than for a Multimode-SI-POF.

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Figure 2.25 shows the exponentially formed signal loss in relation to the bend-ing radius for a POF with a core radius rco= 0.49 mm and describes the ray path for a bent fiber when the ray goes under refraction due to the curved fiber [6], [2], [15].

Figure 2.25: Macrobends: a) Ray path in a curved fiber b) Power loss as a function of the bending radius, adapted from [2].

The signal loss during bending mainly depends on the ambient temperature ϑ, the bending radius R, the core diameter dco, the refractive index of the core nco and the wavelength λ of the transmitted light.

2.6.2. Effects on Numerical Aperture

The numerical aperture of a fiber with a constant length, bending radius and a descending bending angle is reduced under curvature. A signal attenuation on the fibers output is induced that proves the existence of a dependence between the light intensity of the fibers output and a bending angle, as depicted on the following figure 2.26.

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Figure 2.26: Reduction of numerical aperture of a curved fiber, adapted from [16].

The NA as a function of the bending radius and the fiber core radius is defined as: N Abent= s n2 co− n2cl· 1 + rco Rbent (2.18) where rcois the core radius of the fiber and Rbentthe bending radius. The quantities of the fiber parameters utilized in the present project are as follows:

N A = 0.5, nco= 1.49, ncl = 1.417, rco = 0.49 mm, Rbent = 20 mm

The insertion of the values in equation (2.18) for the numerical aperture of a bent fiber leads to:

N Abent = s 1.492_{− 1.417}2_· 1 + 0.49 mm 20 mm = 0.40 (2.19)

The previous calculation of the NA in (2.19) proves the decrease of the numerical aperture for a reduced bending radius. The amount of light intensity on the fiber output under curvature is mainly influenced by the core diameter and the refractive indexes of the core and cladding [24].

2.6.3. Effects on Modes

The analysis of light rays under curvature is usually performed by the Ray-tracing method. The cross-sections of the fiber are considered before and after bending for

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a calculation of guided ray paths inside a curved fiber. The propagation sense of guided light rays is in direction of the core-cladding axis in a straight fiber which serves as a reference axis for the calculation of guided rays inside the fiber core [6].

The bending process leads to a rotation of the core-cladding axis by the amount of the bending angle α. Guided light rays still tend to propagate in the same direc-tion as in the condidirec-tion of the relaxed fiber and mode conversion occurs. Guided modes are transformed into Radiation Modes and are absorbed by the cladding or leave the core and convert into Cladding Modes, as previously described in section 2.2.7. The ray path inside the bent fiber core is illustrated on the following figure 2.27 [6].

Figure 2.27: Ray path in a curved fiber a) Propagation direction before bending b) Altered propagation direction after bending, adapted from [6].

The distribution of modes at the end of the curved fiber with a large NA is demonstrated on the following figure 2.28. Outer modes own a stronger tendency to convert into radiation modes for lower numerical apertures [6].

Figure 2.28: Detailed ray path in a curved fiber: a) Launched light rays b) Rays that exceed the critical angle of total reflection behind the bend c) Guided rays after the bend, adapted from [6].

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Theoretical Approach of the Ray Path within a Curved Fiber

A theoretical approach for the calculation of the transmitted energy in a bent fiber was realized in [9]. The calculation is based on the Ray-tracing model and under assumption of a finite cladding thickness, thus light can travel into the cladding without beeing absorbed or totally lost.

The ray theory describes the ray tracing characteristics as follows:

A Mode reaches the core-cladding interface and is divided into a Refracted Mode and a Cladding Mode or Tunneling Mode. The refracted mode, produced at the outer core-cladding interface is depicted as ’1’ on the following figure 2.29. The cladding mode travels into the inner core-cladding interface, depicted as ’2’ on the following figure 2.29 [9].

The Mode characterized by a thicker line, traveling inside the core on figure 2.29 is illustrated under assumption that the cladding thickness is finite. That assump-tion forces partially refracted or radiated modes to be absorbed by the cladding on the core-cladding interface. Reflected modes return back into the core under conditions of a real fibers. The number of refracted and tunneled rays grows with 2n for a n-times-looped fiber [9].

Figure 2.29: Ray path in a curved fiber of finite cladding thickness: 1) Refracted mode 2) Cladding mode, adapted from [9].

The transmission energy Tr of the refracted modes is based on the classical Fres-nel’s coefficient in scalar approximation. The transmission energy of the cladding modes is low, by Tt ≈ 10−8, in comparison to the transmission energy of the re-fracted modes Tt and therefore Tt = 0 is assumed. The detailed calculations of these transmission energies are presented in [9]

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Calculation of Number of Modes with Parameters of current Appli-cation

The quantities of the fiber parameters, utilized in the current project are as follows:

N A = 0.5, nco= 1.49, ncl = 1.417, rco = 0.49 mm, Rbent = 20 mm

The normalized frequency V for a relaxed fiber is derived as follows:

V = 2 · π · rco

λ · N A =

2 · π · 490 µm

0.6328 µm · 0.5 = 2432.65 (2.20) The number of modes is significantly reduced by the fact of the reduced numerical aperture, as proven in equation (2.19) for the numerical aperture of the bent fiber. The diminished normalized frequency V for the reduced N A = 0.4 is calculated as follows:

V = 2 · π · rco

λ · N A =

2 · π · 490 µm

0.6328 µm · 0.4 = 1946.11 (2.21) The number of modes for the relaxed fiber is calculated as follows:

N = V 2 2 = 2432.652 2 = 2.96 · 10 6 _(2.22)

The number of modes for the bent fiber is calculated as follows:

N = V 2 2 = 1946.112 2 = 1.9 · 10 6 _(2.23)

The previous calculations of the numerical aperture (2.19), the normalized fre-quency (2.20) and the number of modes (2.23) prove that a decreasing bending angle leads to a reduced numerical aperture and secondly a descending number of modes.

Rbent ↓ ⇒ N A ↓ ⇒ V ↓ ⇒ N ↓

2.6.4. Effects on the Amount of Speckles

The amount of speckles and its intensity distribution varies in dependence to the amount of curvature. The measurement results proved that the amount of speckles

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and the speckle-pattern intensity reduces for a growing bending angle, by the fact of a decreasing numerical aperture.

The following equations demonstrate the influence of the curvature on the amount of speckles. The total amount of bright and dark speckles in a defined speckle pattern array is defined as:

Npattern =

N A2 _{· d}2 co

λ2 (2.24)

under the utilization of the physical quantities of the present project:

Npattern = N A2_{· d}2 co λ2 = 0.52_{· 980}2 _µm 0.63282 _µm = 599 · 10 3 _(2.25)

The amount of speckles in a defined speckle-pattern area for the reduced N A = 0.4 of the bent fiber is calculated as follows:

Npattern = N A2_{· d}2 co λ2 = 0.42_{· 980}2 _µm 0.63282 _µm = 383.7 · 10 3 (2.26)

Equation (2.18) of the numerical aperture under curvature, equations (2.24) and (2.26) prove the reduction of the amount of speckles for a decreasing bending radius.

Rbent ↓ ⇒ N A ↓ ⇒ Npattern ↓

2.6.5. Effects on inner Light Intensity Distribution

The mode distribution on the fibers end face during curvature is explained in this section, based on research results of [24].

The incident ray crosses the whole section in a straight fiber whereas in a bent fiber it crosses only the half of the cross section, as depicted on figure 2.30. The power distribution of the inner fiber core changes during the propagation path and concentrates on one side of the fiber over the length. The concentration of light at the end face of the fiber is analyzable graphically by image processing techniques.

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Figure 2.30: Intensity distribution in a a curved fiber: a) Ray Path b) Light intensity distribution over fiber cross section at different length steps, adapted from [24].

The light intensity diminishes in a defined area on the fibers end face with an ascending bending angle, as described in [24] and [25]. The position of the energy concentration field on the fibers end face is constant. For a determination of the light intensity in relation to the bending angle, a defined region of the fibers end face can be observed graphically. The simulation results of [24] for the energy distribution on the fibers end face for different bending radii are illustrated the following figure 2.31. As observable, the field intensity at a constant position declines with an decreasing bending radius.

Figure 2.31: Field distribution of the fundamental mode versus bending radius by simulation: a) Rbent= 5 m b) Rbent= 0.05 m c) Rbent= 0.005 m, adapted from [24].

The theoretical and simulated results are proven by a practical demonstration in [24]. 2.32. The fiber was maintained in a curved position by epoxy glue at a bending radius of Rbent= 5 mm, as illustrated on figure 2.32a. Subsequently, the fiber was cut and polished in the middle of the bending arc as demonstrated on 2.32b thus, the energy distribution on the fibers end face was observable with a microscope, as illustrated on 2.32c.

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Figure 2.32: Experimental setup to detect field distribution on fiber end face: a) Fixation of bent fiber in epoxy glue b) Cut of fiber to analyze end face c) Microscope image of speckle-pattern at fiber end face, adapted from [24].

2.6.6. Effects on Light Intensity for Multiple Looped Fiber

The transmission loss Tt represents the major part of signal attenuation for a n-looped fiber, as previously described. That part of energy loss is comparatively high for a low amount of loops. Refraction modes lose most of their energy after several loops, due to the propagation path length. Afterwards, the secondary losses such as cladding modes or tunneling modes are detectable. This physical effect ex-plains the disproportional signal attenuation in relation to the amount of loops [9].

Signal Attenuation as a Function of Amount of Loops

The following figure 2.33 represents the output power over the wavelength for different amounts of fiber loops. As can be seen, the signal attenuation between n = 5 and n = 10 loops is not the doubled as expected. The signal attenuation in relation to the amount of loops is nonlinear in the region from n = 1 to n = 10, as depicted on figure 2.33. The small wavelength dependence is referred to tunneling rays and core-refractive index dependence over the wavelength nco≡ nco(λ) [9].

Figure 2.33: Output power as a function of wavelength and number of fiber turns at a bending radius Rbent= 5.1 mm and core diameter dco= 1 mm [9].

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The attenuation after n = 8 for a bending radius R = 8 mm, demonstrates continuity on figure 2.34. The parameters of the fiber under test are dco = 980 µm, cladding thickness = 10 µm, nco= 1.492, ncl = 1.402.

Figure 2.34: Output power loss in relation to amount of fiber turns [9].

Signal Attenuation as a Function of Amount of Fiber Loops and Bending Radius

After n = 5, only slight changes in the signal attenuation for bending radii higher than R = 5.10 mm are detectable on the following figure 2.35. The attenuation for a descending bending radius rises strongly by an growing amount of turns. The sensitivity of a curvature sensor consisting of a looped fiber is improved by the the reason of the amplified attenuation.

Figure 2.35: Output power loss in relation to amount of fiber turns for different bending radii [9].

Signal Attenuation of Looped Fibers of different Manufacturers

Figure 2.36 and figure 2.37 represent the relation between the signal attenuation of looped fiber of different manufacturers in relation to the bending radius. A

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Standard POF PFU-CD-1000 characterized by a commonly high NA is utilized in figure 2.36.

Figure 2.36: Output power loss versus inverse bending radius for different amount of fiber turns of a PFU-CD1000 [6].

In figure 2.37 a POF NC-1000 characterized by a relatively small NA was utilized. The POF NC-1000 owns a stronger signal attenuation in comparison to the PFU-CD-1000. The signal attenuation grows significantly with the number of turns at a constant bending angle. Generally, the signal attenuation rises strongly for a growing number of turns and bending angle.

Figure 2.37: Output power loss versus inverse bending radius for different amount of fiber turns of a NC-1000 [6].

2.6.7. Repeated Curvatures in Long-Time Range

A repeated bending test of a POF over a long-time range was performed in [12] and the results revealed that the signal attenuation rises rapidly with a diminishing bending radius over the time, as depicted on the following figure 2.38. A lower bending radius generates higher signal attenuation for several repeated bendings. A significant attenuation after 1000 bends at a bending radius of 5 mm is noticed.

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A bending radius of 10 mm has no significant effect on the signal attenuation as demonstrated on figure 2.38.

Figure 2.38: Signal attenuation as a function of the bending radius and amount of repeated bendings [12].

2.6.8. Repeated Curvatures in Short-Time Range

The elasticity and mechanical memory of the fiber cause deviations of signal re-sponse in high frequent repeated bending operation. Assuming the following pro-cedure:

A fiber is curved in one direction to an angle α and rested for some seconds and is subsequently turned back to the relaxed position. After a time lapse of several seconds, the process is repeated. Both signal responses for the same bending an-gle α represent a deviation, traced back to the mechanical memory of the fiber. This effect was proven in [12] and is illustrated on figure 2.39, where the repeat accuracy for a bending radius of 10 mm was examined.

Figure 2.39: Signal attenuation as a function of the bending radius in bending-straightening mode [12].

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2.6.9. Practical Implementations based on Curvature Analysis

The previously described physical effects on a curved fiber serve as a knowledge base for the design of the experimental setup.

The speckle pattern analysis for the determination of the bending angle of the curved fiber, are performed by the knowledge of the research results revealed in [24]. The speckle-pattern that is projected on the fiber end face changes visible during curvature and can be analyzed graphically by the observation of a defined region of interest of the speckle-pattern.

The signal attenuation is significantly amplified by looping the fiber for several times. This effect is utilized as an adjustable parameter for the curvature sensor sensitivity. A higher signal attenuation is generated for a looped fiber during cur-vature and therefore, the measurement of signal in relation to the bending angle is more precise by the fact of the stronger attenuation.

2.7. Relevant Research and State of the Art

2.7.1. Technical Evolution of the POF

The demand of POFs raised rapidly in the last decades according to the reduction of impurities in the material by an improved manufacturing process and mate-rial compositions. The fiber bandwidth increased by the simultaneous diminish of signal attenuation. Sensors based on POF, find application in environmental, biological and chemical research, structural health monitoring, medicine, civil en-gineering, aeronautics, aerospace and automobile industry [26], [14], [15], [2]

The physical characteristics such as lightweight, electromagnetic interference im-munity, chemical resistance, mechanical robustness and flexibility made the POF more attractive for industrial applications. Manufacturing of the POF is character-ized by low installation and linking effort arising from a high numerical aperture, low bending radius and large diameter. Comparatively low expenses for material and elementary development equipment make the processing of the POF feasible [2], [1].

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2.7.2. Overview of POF - Based Sensors

The POF-based sensors utilized in industrial applications are frequently applied for gauging physical related parameters such as strain, pressure, stress, vibration, current, rotation, displacement, temperature, leakage, bending angle, biomedical parameters, deformation, [2], [1], [27], [28], [26], [15], [6], [14]. Special applications such as acceleration measurement [29], determination of surface roughness [30], determination of thickness of a transparent plate [31] or glass damage detection [6] were developed. For a better overview, POF-based sensor examples and their working principle in industrial applications are presented:

Strain Sensor

The physical measuring parameter is often transformed in another quantity to be measured as realized in [24] where the strain applied on a elastic belt is trans-formed into a curvature of the fiber by special fiber arrangement. A dependence between the strain and the signal attenuation is achieved by this method.

Force Sensor

A POF is arranged in 20 loops over a hollow flexible cylinder. Lateral forces ap-plied on the cylinder cause a deformation of the cylinder and a signal attenuation on the fiber output. The applied force causes a displacement and can be physically transformed in pressure, force or displacement, as presented in [10]. The signal attenuation is disproportional to the amount of loops and a non-linear characteris-tic of the attenuation as a function of the deformation of the cylinder was revealed.

Wing-Deformation Sensor

A rotor wing deformation sensor of wind power plants was developed by Photon Project and supported by Bavarian Research Foundation is presented in [6]. The POF is fixed on the rotor wing and a phase modulated signal is propagated through the fiber. A wing deformation provokes a phase shift between the modulated ref-erence signal and the curved POF mounted on the wing. A linear characteristic of the deformation as a function of the phase shift is revealed.

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Temperature Sensor

A POF-based temperature sensor consists of a macrobend loop and its sensitivity is adjusted by the radius of the macrobend as described in [18]. The signal loss raises with an increasing temperature and its sensitivity is adjusted by the bend-ing radius. A similar principle with multiple macrobend loops for the temperature measurement is presented in [19]. Both researches revealed the dependence of bending losses with the temperature and bending radius.

Humidty Sensor

A POF-based humidity sensor is realized by the analysis of the refractive index alteration by absorbed water of the fiber core. Certain molecules of the polymer material swell up when the fiber absorbs water and the change of the refractive index leads to a different signal attenuation on the fiber output [6].

The major part of the POF-sensors is based on light intensity modulation as demonstrated by the preceding sensor examples. The loss in light intensity is of-ten proportional to the physical related measured parameter which simplifies the measurement of the signal response. However secondary losses caused by absorp-tion, scattering and radiation are included in the resulting measured parameter and represent a negative influence on the accuracy and reliability of the sensor [1].

The signal on the Multimode-fiber output can be analyzed with a CCD-camera instead of a photodiode or phototransistor as realized in the following sensor ex-amples. A granular speckle-pattern can be captured and analyzed with digital image processing techniques to determine the change of physical parameters as described in the following section.

2.7.3. POF - Sensors based on Speckle-Pattern Analysis

Modal Noise occurs only in Multimode-fibers and is also known as Mode-Distribution Noise or Speckle-Noise. Each light ray contains a own power distribution over the fiber cross section. The power distribution between light rays are defined as Speckle-Pattern and it varies with external changes such as temperature,

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wave-length of light source and vibration while the allover intensity of the speckle-pattern remains unchanged [2], [6]. Several image processing techniques for the analysis of the speckle-pattern were developed as presented in this section.

Fiber Elongation Sensor

A strain gauge for the determination of the fiber elongation in the µm-range is based on a self-developed correlation factor between two speckle-pattern images [20]. A comparison of the speckle-patterns intensity distribution before and after deformation generate a spatial correlation factor defined by a given formula. A decreasing correlation factor represents a lower similarity between the images and demonstrates a higher grade of elongation. The measuring method is character-ized by low computing effort, adaptability, high precision and reliability.

Temperature Sensor

The spatial correlation calculation between two speckle-pattern images for tem-perature measurement is described in [13] and compared with the Mean Speckle Intensity Variation (MSV) image processing technique. A subsequent image is subtracted from a reference image and afterwards integrated. Both techniques are characterized by a certain adaptability and high precision.

Vibration Sensor

The measurement of vibration by the application of the speckle-pattern image difference technique is presented in [32] where the variation of the speckle-pattern intensity distribution is examined. The technique is characterized by computa-tional low effort and simplicity in implementation.

Specklegram Sensor

A wavelength domain multiplexed fiber specklegram sensor is presented in [33] that analyzes the influence of the wavelength on the signal response for a POF Multimode-Step-Index Fiber under perturbation. Green light with a wavelength of 532 nm and red light with a wavelength of 632.8 nm are coupled together over an optical 50/50 coupler into a fiber of 1 m length and a diameter of 980 µm, as

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depicted on figure 2.40. A CCD-camera generates speckle-pattern images with a resolution of 400 x 400 pixels on the fibers end face.

Figure 2.40: Specklegram measurement setup [33].

The images are scaled to its mean value to compensate differences in light energy between the color channels red, green and blue. The employment of an RMS-contrast to the images improved the visibility of the speckles. The specklegram of the red channel demonstrated a better contrast than the green channel as illus-trated on figure 2.41

Figure 2.41: Equalized specklegrams of a) Red channel b) Green channel [33].

The images are analyzed with the speckle-pattern image difference technique for each color channel and subsequent images before and after perturbation are com-pared. The image differences for each channel was recorded and analyzed as de-picted on figure 2.42.

Figure 2.42: Signal responses of specklegram sensor for perturbation on a) The common fiber and b) The fiber of red light channel, adapted from [33].

Polymer optical fiber curvature measuring technique based on speckle pattern image processing

POLYMER OPTICAL FIBER CURVATURE

MEASURING TECHNIQUE BASED ON SPECKLE

PATTERN IMAGE PROCESSING

Contents

1. Introduction

1.1. Motivation

1.2. Scope of The Work

1.3. Objectives

1.4. Document Structure

2. Properties of Polymer Optical Fiber

2.1. The Multimode Polymer Optical Fiber

2.2. Light Propagation in POF

2.3. Attenuation processes of the POF

2.4. Signal Attenuation Induced by Ambient

2.5. Speckles

2.6. Analysis of Fiber under Curvature

2.7. Relevant Research and State of the Art